Question: Simplify the following expression: $\sqrt{27}+\sqrt{12}-\sqrt{48}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{27}+\sqrt{12}-\sqrt{48}$ $= \sqrt{9 \cdot 3}+\sqrt{4 \cdot 3}-\sqrt{16 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{3}+\sqrt{4} \cdot \sqrt{3}-\sqrt{16} \cdot \sqrt{3}$ $= 3\sqrt{3}+2\sqrt{3}-4\sqrt{3}$ Finally, simplify by combining the terms. $= ( 3 + 2 - 4 )\sqrt{3} = \sqrt{3}$